Combinatorial Trigonometry with Chebyshev Polynomials

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Larry Ericksen
Pallavi Jayawant, Bates College
Mark Shattuck, University of Tennessee - Knoxville

Document Type

Article

Department

Mathematics (HMC)

Publication Date

8-2010

Abstract

We provide a combinatorial proof of the trigonometric identity cos(n_{θ) =} T_ncos(θ),
where T_n is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.

Comments

First published in Journal of Statistical Planning and Inference, Proceedings of the 6th International Conference on Lattice Path Combinatorics,, Vol. 140, Issue 8, pp. 2157-2160, 2010.

This article is also available at http://www.sciencedirect.com/science/article/pii/S0378375810000224.

Rights Information

© 2010 Elsevier B.V.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.jspi.2010.01.011

Recommended Citation

Benjamin, A.T., Ericksen, L., Jayawant, P., & Shattuck, M. (2010). Combinatorial trigonometry with Chebyshev polynomials. Journal of Statistical Planning and Inference, 140(8): 2157-2160. DOI: 10.1016/j.jspi.2010.01.011.